CorollaryStatement: Literature-sourcedProof: AI-adaptedprecheck pass

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Every affine scheme is quasi-compact

Assume the Axiom of Choice. Every affine scheme is quasi-compact.

Given: The Axiom of Choice (The Axiom of Choice) and an affine scheme $X$ .

[F1]

Under the Axiom of Choice, every distinguished open of an affine spectrum is quasi-compact (Every distinguished open of an affine spectrum is quasi-compact).

technique · direct

1.1givenchoose

Choose an isomorphism $X ≅ Spec A$ from affineness.

1.2F1given

The whole spectrum is $D (1)$ , which is quasi-compact by [F1] under the assumed Axiom of Choice. This is the only use of AC in this argument.

2.1step 1.1step 1.2∎

Its homeomorphic copy $X$ is quasi-compact.

Depends on